|Ever since the pragmatic turn took place in the 1960s, linguists have been exploring the pragmatic level of language, paying attention to concepts such as speaker’s intention or meaning in context. However, these notions were still largely overlooked, if not ignored in language teaching itself for many subsequent years, reducing language teaching to studying language forms in isolation, concentrating mainly on memorizing vocabulary lists and practicing grammar rules. The growing trend of extending this framework by pragmatic competences, i.e. “actual language use in the (co)construction of text”, can be demonstrated by the fact they are among the three main competences listed in the CEFR. Indeed, lack of understanding of the pragmatic aspects of language use may result in the so-called “pragmatic failure” (Thomas 1983), which makes communication much more difficult than by making a grammar mistake or mispronouncing a word. To some extent, pragmatic competences have been addressed in respect to teaching general English (e.g. Kasper 1997 and 2001, Holtgraves 2007, Taguchi 2009); nevertheless, they have not been examined as regard ESP and EAP, despite their major role in many LSP as well as LAP contexts. Therefore, this paper addresses the issue of how pragmatic competences are presented and taught in several ESP (English for Psychology, Cambridge English for the Media, Cambridge English for Human Resources) and EAP (Cambridge Academic English and Oxford EAP) textbooks. The aim is to find out the extent to which they are dealt with in these textbooks as well as to identify the main pragmatic fields under examination. In conclusion, the author, who teaches both EAP and ESP courses at university, would like to shed new light on the so far rather neglected, yet essential pragmatic competences in tertiary education textbooks.